Effects of external noise on anomalous diffusion in Hamiltonian dynamical systems

The effect of external noise on diffusion processes in a Hamiltonian system with an external force is studied. This is represented by the standard map with an external force. When external noise is applied to the system, we f ind strongly enhanced diffusion in a parameter range in which anomalous dif fusion occurs. Although chaotic orbits are not deterministic in a strict se nse, because the system includes noises, they exhibit Levy flight due to th e intermittent sticking to transient tori.